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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 23, NO. 1, JANUARY 2008 495 Adaptive Modulation Control for Multiple-Phase Voltage Regulators Shangyang Xiao, Weihong Qiu, Greg Miller, Thomas X. Wu, Senior Member, IEEE, and Issa Batarseh, Fellow, IEEE Abstract—This letter presents an adaptive modulation control (AMC) method which has proven to be effective in achieving high bandwidth designs as well as stabilizing the control loop during large load transients. The AMC adaptively adjusts control bandwidth by changing the modulation gain, depending on different load conditions. With the AMC, a multiphase voltage regulator can be designed with an aggressively high bandwidth, while in heavy load transients where the loop could be potentially unstable, the bandwidth is lowered. Therefore, the AMC provides an optimal means for robust high-bandwidth design with excellent transient performance. It is a type of non-linear control designed for, but not limited to, multiphase voltage regulators with droop control. Detailed analysis of the operational mechanism is presented. Experiment results are included to verify the analysis. Index Terms—Adaptive modulation control (AMC), bandwidth, multiphase voltage regulator (VR), transient response. I. INTRODUCTION N EXT generation microprocessor (Vcore) requirements for high-current slew rates and fast transient response, together with low output voltages, have posed great challenges on voltage regulator (VR) design. For today’s microprocessors, the operational current may exceed 100 A with voltages in the 1 to 1.5 V range, while the slew rate of the transient current can be over 1 A/ns –. Much effort has been made, such as application of novel topologies, advanced devices, and control schemes, to meet the stringent Vcore specifications for transient response –. Droop control, also referred to as adaptive voltage positioning (AVP) in –, is popularly implemented to achieve a cost-effective voltage regulation. With droop control, the output voltage will droop when the load current increases, resulting in improved voltage tolerance. As a result, droop control allows more voltage deviation than voltage-mode control; therefore a significant number of the output capacitors can be saved for the same output voltage specifications. It is desired to push the bandwidth as high as possible to achieve a fast transient response. However, the maximum system bandwidth is limited by the switching frequency. Typically the transient response obtained from a system with higher switching frequency is better than that with lower switching frequency. For multiphase voltage regulators used in low-voltage applications, the effective frequency of the output voltage ripple is equal to the product of the phase number and phase-switching frequency, as shown in Fig. 1(a). Based on conventional loop analysis, the bandwidth of multiphase voltage regulators could be pushed close to the phase-switching frequency. Manuscript received March 22, 2007; revised June 8, 2007. Recommended for publication by Associate Editor R. Zane. S. Xiao, W. Qiu, and G. Miller are with the Intersil Corporation, Milpitas, CA 95035 USA (e-mail: [email protected]). T. X. Wu and I. Batarseh are with the School of Electrical and Computer Engineering University of Central Florida, Orlando, FL 32816 USA. Digital Object Identifier 10.1109/TPEL.2007.912947 Fig. 1. Interleaved operation for multiphase voltage regulators. (a) Interleaved operation waveforms. (b) Bode plot of power stage. For some advanced control schemes like adaptive phase alignment (APA) in , however, all phases are turned on simultaneously to increase the current slew rate during large load-insertion transients. In this case, the effective frequency of the output ripple will be reduced to the phase-switching frequency, as shown in Fig. 2(a). In frequency domain, a multiphase VR with APA control during transients shows a different gain-phase relationship from a regular multiphase VR. For a regular multiphase VR, the abrupt gain drop and phase delay caused by the aliasing effect  occurs at phase number times the phaseswitching frequency, as shown in Fig. 1(b). For a VR in simultaneous operation, however, the gain and phase dips occur at the phase frequency, as shown in Fig. 2(b). It behaves like a single-phase voltage regulator. With a high bandwidth design, this can be disastrous if care is not taken: sideband components induced by the aliasing effect can result in system instability 0885-8993/$25.00 © 2007 IEEE Authorized licensed use limited to: University of Central Florida. Downloaded on January 15, 2010 at 14:12 from IEEE Xplore. Restrictions apply. 496 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 23, NO. 1, JANUARY 2008 Fig. 3. Simplified model for voltage regulator with droop control. Fig. 2. Simultaneous operation for multiphase voltage regulators. (a) Simultaneous operation waveforms. (b) Bode plot of power stage. . Motivated by the demand for a control method which is able to facilitate a high-bandwidth design as well as stabilize the loop during large load transients, adaptive modulation control (AMC) is proposed in this letter. II. MECHANISM OF ADAPTIVE MODULATION CONTROL The block diagram of a typical voltage regulator with droop control is shown in Fig. 3. The inductor current, , is sensed and being the current sense gain. fed to the error amplifier, with , flows through and develops a This sensed current, . voltage droop across Based on the simplified model for multiphase VRs with droop control in , the voltage loop gain can be expressed by (1) where is the current sense gain, is the input voltage, and are the power stage parameters, and are the compensation parameters. Fig. 4. Simplified Bode plot of the loop gain with droop control . is the modulation gain, which is inversely proportional to the (referred to GND) of the ramp signal. peak-peak voltage The simplified Bode plot of droop control is illustrated in Fig. 4. It is found that there exists a flat range between the . Therefore, the bandwidth can ESR zero and the pole be adjusted by varying the pole frequency. Since the pole is determined by the output inductance, modulation gain and other parameters, a change of the modulation gain will have a direct impact on the system bandwidth. Adaptive modulation control is proposed by this motivation. The concept is to design an aggressively high bandwidth for steady-state operation, while decreasing the bandwidth by reducing the modulation gain when phases are on simultaneously. If the modulation will be pulled to a lower frequency, thus gain is reduced, reducing the high-frequency gain while keeping the low-frequency gain unchanged, as shown in Fig. 4. For a multiphase VR with droop control, the decrease of high-frequency gain means a decrease of bandwidth and possibly an increase of phase margin. During a large load transient, a corresponding large perturbation will be introduced to the output. This large perturbation in time domain can be transformed into large high-frequency components in the frequency domain. Since the feedback control loop functions as a low-pass filter, these high-frequency components and their associated sideband frequencies can not be damped if the bandwidth is too high . With AMC, the loop gain at a Authorized licensed use limited to: University of Central Florida. Downloaded on January 15, 2010 at 14:12 from IEEE Xplore. Restrictions apply. IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 23, NO. 1, JANUARY 2008 497 Fig. 6. Circuit implementation of AMC. Fig. 5. Operational waveforms of AMC. high frequency range is reduced to attenuate the high-frequency components in large load-transient events. Time-domain investigation of AMC leads to the discovery that AMC shows great advantages in removing undesired voltage spikes during large load-insertion transients. Fig. 5 shows the operational waveform comparisons of a two-phase VR with traditional trailing edge modulation (TEM) and with AMC for a load-insertion case. The TEM has a fixed ramp signal RAMP1 (solid line), while the AMC has a flexible ramp signal RAMP2 (dashed line). For traditional TEM, the clock (CLK) signal initiates the pulsewidth modulation (PWM) turn-on, while the PWM is turned off as the RAMP1 signal intersects the output voltage of the error amplifier (COMP). which can The total inductor current is charged at slew rate be expressed as (2) and represent output voltage and phase inducwhere tance, respectively. And N is the phase number. When APA  is triggered, the system turns on all PWMs simultaneously. The output inductance is equivalent to N inductors in parallel. Therefore, the sum of all inductor currents has approximately N times the slew rate of that of a single inductor, i.e., (3) where represents the inductor current slew rate for simulis taneous operation. For low-voltage applications where is approximately times . In this much less than case, the effective charging time is reduced by a factor of . As a result, the PWM turn-off of the simultaneous operation is expected to be sooner. However, due to the fixed ramp signal of the traditional modulator, the turn-off timing of PWMs sees no change, even though all phases are on simultaneously under large load-insertion events. Consequently, significant turn-off delay is introduced during load-insertion transients. This turn-off delay causes extra energy stored in the output inductors to continue charging the output capacitors, resulting in undesirable results, such as ring-back and longer settle-down time, etc. With AMC, the optimal slew rate of the ramp signal is adjusted, based on the number of on phases, as shown in the simplified circuit implementation in Fig. 6. If PWM pulses of both phases are on simultaneously, the ramp signal rises with twice the slew rate of the ramp in normal interleaved operation, as the dashed line shows in Fig. 5. In this manner, the modulator Fig. 7. Pspice simulations for VRs without and with AMC, using LGA775 Socket and VTT Tool simulation model provided by Intel. System parameters: V 12 V, V 1.2 V, I 50 A, L 310 nH, C 5 680 F 12 16 F. (a) Simulated transient response without AMC. (b) Simulated transient response with AMC. = + 2 = = = = 2 gain decreases by half under a transient event. And the PWM is terminated at t1 rather than t2, resulting in a reduced turn-off delay. Since AMC is activated by large load transients, it will not sacrifice steady-state stability. On the contrary, compared with normal design of the same bandwidth as AMC, during large load transients AMC can achieve faster transient response due to its higher steady-state bandwidth. Fig. 7(a) and (b) shows simulation results for a three-phase droop-control VR without and with the AMC scheme. The inductor currents, PWMs, and output voltages are marked as , PWM1, PWM2, and on the waveforms, respectively. During a large load transient, all phases are on simultaneously for fast transient response. The first voltage spike is determined by ESR and ESL. Following the first spike, for traditional trailing-edge PWM modulation control in Fig. 7(a), there is significant voltage ring-back due to extra energy in the inductors Authorized licensed use limited to: University of Central Florida. Downloaded on January 15, 2010 at 14:12 from IEEE Xplore. Restrictions apply. 498 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 23, NO. 1, JANUARY 2008 Fig. 9. Experimental measurement of loop gain and phase for VR with AMC enabled and disabled. IV. CONCLUSION Fig. 8. Experimental result comparison, using Intel LGA775 VTT tool. System 12 V, V 1.2 V, I 95 A, L 315 nH, C parameters: V 5 560 F OSCON 12 22 F MLCC 6 10 F MLCC. (a) Transient response without AMC. (b) Transient response with AMC. 2 = + 2 = = + 2 = = during the transient event. AMC removes the turn-off delay by increasing the ramp slew rate; therefore the ring-back voltage is avoided and the system can settle down in a short time, as shown in Fig. 7(b). III. EXPERIMENT VERIFICATION A 300 kHz four-phase VR designed with very high bandwidth and excellent transient response is built to verify AMC. The measured transient responses in time domain for the VRs without and with AMC are shown in Fig. 8(a) and (b). The and the lower upper waveforms represent the output voltages . From the experiment waveforms represent load currents comparison, it is found that excellent transient performance is achieved for the voltage regulator with AMC. The voltage spikes are successfully suppressed under a large load transition. Measured Bode plots of the closed loop system shown in Fig. 9 illustrate how AMC adaptively adjusts the control bandwidth. The grey curves represent gain and phase of the loop during steady state (AMC is not triggered), while the black curves are gain and phase of the loop with AMC enabled. When AMC is not triggered, the bandwidth is about 420 kHz and the phase margin is 61 . During a large load transient, AMC pulls down the modulation gain and drops the bandwidth to 94 kHz. Hence, the phase margin is boosted to 139 . Traditional PWM modulation schemes fail to achieve a robust high-bandwidth design and remove voltage ring-back during large load transients. The proposed AMC provides an effective solution by adaptively changing the modulation gain during large load transients. With AMC, it is possible to push the bandwidth above the switching frequency for multiphase VR applications with robust operation under all conditions. Simulation and experimental results have verified the proposed AMC scheme and corresponding analysis. REFERENCES  W. Qiu, Z. Liang, and M. 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